Comparative analysis of the relaxation properties of virgin and recycled polypropylene

Transcription

1 Plasticheskie Massy, No. 6, 29, pp Comparative analysis of the relaxation properties of virgin and recycled polypropylene A.V. Golovanov, M.N. Popova, 2 V.A. Markov, 2 O.V. Kovriga, 2 and A.A. Askadskii 2 V.V. Kuibyshev State Building University, Moscow 2 A.N. Nesmeyanov Institute of Heteroorganic Compounds, Russian Academy of Sciences andrei@ineos.ac.ru Selected from International Polymer Science and Technology, 37, No. 3, 29, reference PM 9/6/4; transl. serial no. 62 Translated by P. Curtis Abstract The thermomechanical and relaxation properties of virgin and recycled polypropylene are presented. A comparative analysis is made of the stress relaxation parameters in the linear and non-linear region of mechanical behaviour, which were determined using a specially written computer program. At present, materials that are produced using polymer waste are being used increasingly in various areas of the national economy. This method of recycling polymer waste is expedient both ecologically and economically. The present research was conducted on polypropylene (PP), both virgin PP and PP recycled from spent materials. The recycled PP production process is presented in Figure. It consists of the following operations: the sorting of the polymer waste (unit ), its washing, grinding, and crushing (units 2 to 5), granulation (unit 6), and the manufacture from the granules, by injection or transfer moulding, of articles of different designation. The PP waste was mainly waste from preventive medicine establishments (PMEs). According to SanPiN , which gives the PME waste classification (making it possible to ascribe a risk characteristic to any form of waste and to organise correctly measures for collection, sterilisation, and recycling), waste is accepted from establishments only with a disinfection certificate, with indication of the person responsible for the disinfection and the composition of the disinfecting solution in which the waste was sterilised []. In the present work, a comparative analysis was made of the thermomechanical and relaxation properties of recycled and virgin PP. At the first stage of the investigation, the thermomechanical curves of virgin and recycled PP were measured. Thermomechanical analysis was conducted on a Tsetlin instrument under conditions of penetration of a die of 4 mm diameter with a die load of g. The rate of increase in temperature was 2 deg/min. The thermomechanical curves for specimens of virgin and recycled PP are shown in Figure 2. It is very clear that these curves are practically identical; of note is the fact that the virgin PP exhibits small strains in the range between room temperature and melting point, which is due to the presence of a small amorphous part. The second stage of the research consisted in measuring stress relaxation curves under different Figure. Schematic of the processing of waste PP into granules. waste sorting unit; 2 crusher; 3 washing machine; 4 centrifuge; 5 drying unit; 6 granulator 2 Smithers Rapra Technology T/53

2 Figure 2. Thermomechanical curves of virgin () and recycled (2) PP Figure 5. Stress relaxation curves of virgin ( 3) and recycled (' 3') PP. Strains:, ' 2%; 2, 2' 3%; 3, 3' 4% more rigid. From Figure 5, in which relaxation curves for recycled and virgin PP are combined, this behaviour pattern is very clear. To calculate the relaxation parameters of virgin and recycled PP, use was made of the Boltzmann Volterra equation: Figure 3. Stress relaxation curves of recycled PP. Strains: 2%; 2 3%; 3 4% Figure 4. Stress relaxation curves of virgin PP. Strains: 2%; 2 3%; 3 4% constant strains of 2 4%. These curves are shown in Figures 3 and 4. It can be seen that both the initial and the relaxing stress for recycled PP are considerably higher than for virgin PP under all strains. As the geometric characteristics of the specimens were completely identical, this indicates that recycled PP is considerably t σ = σ T(τ) dt where s is the relaxing stress, s is the initial stress that develops on completion of the instantaneous setting of the strain, T(t) is the nucleus of relaxation, t is the current time, which runs from to t, and t is the final time. Use was made of relaxation nuclei based on an analysis of change in the thermodynamic functions in the course of the relaxation process [2, 3]. According to this analysis, the polymeric material is regarded as consisting of relaxers and non-relaxers, and here, after instantaneous setting of the strain or load, the overwhelming proportion of the material consists of relaxers interacting with each other to form a non-relaxing material. The emergence of kinetic elements of the two grades (relaxers and non-relaxers) and their diffusion in the material lead to the production of entropy of the system, which increases in the course of stress relaxation or creep. As a result of such analysis, two relaxation nuclei, shown below, were proposed. In general form, the relaxation nucleus is as follows: T(τ) = S m αlnα + ( α)ln( α) ln.5 where m = m * T * (τ) dτ (3) () (2) T/54 International Polymer Science and Technology, Vol. 37, No. 9, 2

3 S is the initial entropy of the system (specimen), is Boltzmann s constant, m * is the total number of kinetic units (in the present case, relaxers and non-relaxers per unit volume), a is the proportion of relaxers out of the total number of kinetic units, and T * (t) is the variable part of the nucleus. If the limiting stage of the stress relaxation or creep process is the rate of interaction of the relaxers, then the relaxation nucleus has the form T (τ) = S m (+ k * τ/β) α β ln (+ k * τ/β) α β + (+ k * τ/β) + α β ln (+ k * τ/β) + α ln.5 β (3b) where k * = k n-, n is the order of the reaction, a = -, b = /(n - ), and m = m * T * (τ) dτ If the limiting stage of the stress relaxation or creep process is the diffusion rate of the formed non-relaxers, then the relaxation nucleus has the form T 2 (τ) = S m 2 aτ γ lnaτ γ + ( aτ γ )ln( aτ γ ) ln.5 where g = b/2, and quantity a is determined from the ratio ( a)at b/2 ( < b <, and a is a constant), and The nuclei (3) and (4) make it possible to describe the stress relaxation and creep processes with high accuracy, and also to estimate the physical parameters of the material the quantity A * = m * /S, proportional to the number of inhomogeneities in the material, k *, n, g, a, s (E ), and s (E ), where E is the instantaneous elastic modulus (E = s /e ), s is the quasi-equilibrium stress established at t, E is the quasi-equilibrium elastic modulus, and e is the elastic strain developing under instantaneous loading. Present calculations using the theoretical formulae given above led to the values of the relaxation parameters shown in Table. It must be pointed out that, when the nucleus T (t) is used, the correlation coefficients r are always higher, approaching unity, than when the nucleus T 2 (t) is used. Then, from the positions considered above, the limiting stage of the stress relaxation process is the rate of interaction of the relaxers and their conversion into non-relaxing material. The rate constant of interaction of the relaxers for virgin PP is not dependent on the strain and amounts to. min -. For recycled PP, under small strains, the rate constant of interaction of the relaxers is (4) considerably lower than for virgin PP. Under strains of 3 and 4%, the rate constants of interaction are identical for both PPs. The quantity A *, proportional to the number of inhomogeneities in the material, decreases with increasing strain for virgin and recycled PP. Calculated values of the initial stress s for recycled PP are considerably higher than for virgin PP. The quasi-equilibrium stresses s under small strains are similar to each other, but, under higher strains, recycled PP displays a considerably higher value of s than virgin PP. If experimental values of the initial stress and the stress that develops within 8 min relaxation are compared, it is very clear that, for recycled PP, they are roughly twice as high as those for virgin PP. Thus, recycled PP has a higher elastic modulus than virgin PP, measured not only at a high strain rate but also in the course of the entire relaxation process. This is connected with the more ideal supermolecular structure of recycled PP, which is formed owing to the presence in the PP of impurities in the form of crystallisation nuclei (Figure 6). To establish the elemental composition of the impurities in specimens of virgin and recycled PP, X-ray fluorescence spectra were taken and interpreted on a VRA-3 spectrometer (Germany) with an Mo-tube in a 4 kv 2 ma regime. Spectrometry (intensity measurement) of the discovered lines was carried out, and, after calibration of the spectrometer to PS-based standards, a semi-quantitative calculation of the concentrations of iron, titanium, zinc, copper, calcium, and silicon impurities was carried out. X-ray spectral analysis showed that specimens of recycled PP contain a number of impurities, the nature and number of which is given below. Present in the greatest number are the following impurities (%): Ca.7, Ti.2, Fe.6, and Cu.6. The reason for this seems to be that the given elements are present in the composition of blood and are also generally 2 Smithers Rapra Technology T/55

4 Table. Relaxation parameters of virgin and recycled polypropylene at room temperature Virgin PP Recycled PP 4% 3% 2% 4% 3% 2% Nucleus T (t) k, min r A *, J kg deg/m s, MPa s, MPa Nucleus T 2 (t) g r A *, J kg deg/m s, MPa s, MPa Experimental values s init, MPa s 8, MPa Figure 6. Micrographs of the structure of virgin (a) and recycled (b) PP Figure 7. Relaxation modulus curves of primary ( 3) and recycled (' 3') PP. Strains:, ' 2%; 2, 2' 3%; 3, 3' 4% distributed in nature and can enter the polymer during its processing. The indicated impurities act as nuclei of structure formation of the PP, as a result of which a more ideal crystalline structure may be formed in processed recycled PP (see Figure 6). The degree of crystallinity for virgin and recycled polypropylene amounts to 7 and 83% respectively. As the processing conditions of these specimens were entirely identical (temperature, pressure, holding time, and heating and cooling rate), it can be concluded that the difference in the degree of crystallinity is due to the presence of the impurities mentioned above. For analysis of linear and non-linear mechanical behaviour, we conducted the following calculations based on experimental data on stress relaxation under different strains. Firstly, the relaxation moduli under all strains were calculated, and these are shown in Figure 7. From Figure 7 it is very clear that the relaxation moduli for virgin PP fit fairly well into a narrow cluster, which indicates linear mechanical behaviour. For recycled PP, with increase in the strain, the time dependences of the relaxation modulus decrease considerably, which indicates a non-linear mechanical behaviour. Secondly, using the computer program written by us, we conducted approximation of all the time dependences of the relaxation modulus, and the magnitudes of the excess free volume d in which the elementary act of relaxation proceeds (see below) were calculated. For analysis of the stress relaxation process in the non-linear region of mechanical behaviour, we will make a number of transformations in the functions given above. We will write the Arrhenius equation for the temperature dependence of the rate constant of the reaction: T/56 International Polymer Science and Technology, Vol. 37, No. 9, 2

5 k * = k * e ΔU RT where k * is the pre-exponential cofactor, DU is the activation energy of the process of interaction (in the present case, the interaction of relaxers), R is the universal gas constant, and T is absolute temperature. It is well known that, in the course of deformation of hard polymers, their free volume increases. In the present case this is the free ( empty ) volume comprising the difference between the volume of the body and the Van der Waals volume of the atoms forming the body. Under high strain, when non-linear mechanical behaviour begins to appear, the free ( empty ) volume increases to a fairly high magnitude, which facilitates considerably the jump of kinetic units (relaxers) from one position to another and leads to forced elasticity, i.e. to forced softening of the material. Therefore, if it is assumed that the energy of interaction of the relaxers decreases with increase in mechanical stress, then, with a sufficiently high value of the latter, this may entail the appearance of excess free volume. Hence, the well-known expression for the temperature dependence of the stress relaxation time [4] arises. Thus, we will rewrite equation (5) in the form k * = k * exp ΔU δσ r = k * RT exp ΔU δe ε r RT where E r is the relaxation modulus, DU is the initial energy of interaction of the relaxers, s r is the relaxing stress, e is the constant strain, and d is the excess free volume in which the elementary act of interaction of relaxers occurs. Under small strains (in the linear region of mechanical behaviour), excess free volume still practically is not formed, and then d =, and the rate constant of interaction of relaxers is defined as k * = k * exp( DU / RT), i.e. is not dependent on the mechanical stress. With increase in the specified constant strain e, there comes a point when a large excess free volume appears, which facilitates considerably the interaction of the relaxers and leads to an acceleration of the stress relaxation process. From the positions considered, this is also the transition to non-linear mechanical behaviour. In such a case, quantity k * is not a constant but becomes dependent on the relaxation modulus according to expression (6). Allowance for this makes it possible to conduct the approximation of stress relaxation curves in the non-linear region and at the same time to determine the above-mentioned excess free volume. Before describing the procedure of approximation of the relaxation curves by means of the examined approach [5], we will write the Boltzmann equation in the form E(t) = E E t T(τ) dτ (5) (6) (7) where E is the initial modulus arising after instantaneous setting of the strain, and T(t) is the relaxation nucleus. Experience indicates that the best approximation of the relaxation curves for hard polymers is achieved by using the nucleus T (t), which we will make use of below. Substituting the nucleus T (t) into equation (7), we obtain E(t) = E E S T * m (τ) dτ t (8) where T * (t) is the variable part of the nucleus T (t), described by the equation T * (τ) = (α α )ln(α α ) + ( α + α )ln( α + α ) ln.5 where a is set by the expression (9) α = (+ k * τ/β) β () which holds in the linear region of mechanical behaviour, and a = - [2, 3]. For the case of stress relaxation in the non-linear region of mechanical behaviour, a is defined by the relation α = k * exp ΔU δe ε β r τ RT + β () From a comparison of equations () and () it follows that the term k * exp( DU /RT), which is not dependent on the relaxation modulus E r, corresponds to k * in equation () for the linear region of mechanical behaviour. Thus, it is possible to write a as α = k * exp δe ε β r τ RT + β (2) The approximation procedure consists in determining the d value with which the value of the following function is minimum: 2 Smithers Rapra Technology T/57

6 n ϕ(δ) = (E i,calc E i,exper ) i= where n is the number of experimental points, E i,calc are the relaxation modulus values calculated by means of equation (8), and E i,exper are the experimental values of the relaxation modulus. The algorithm for calculations consists in the following. Experimental values of the relaxation modulus for each stress relaxation curve are input successively into a computer in order of increasing constant strain e. Each curve input, besides the first, is compared with the averaged curve representing mean values of the relaxation moduli from curves input earlier. If, for a newly input curve, each value of the modulus with the same relaxation time is lower than for the averaged curve, and the arithmetic mean relative deviation exceeds the specified value (for example, 5 or %), then such a curve is considered to relate to the non-linear region of mechanical behaviour. Then, for the averaged curve, the usual method is used to calculate the relaxation parameters for the linear region of mechanical behaviour, and, using these parameters, approximation is carried out for a case relating to the non-linear region. The minimum of the function j(d) is sought by numerical integration using Simpson s method. Experiments and calculations showed the following. The quantity d for recycled PP amounts to 8. cm 3 / mol. This value was obtained by approximation of curve 3 in Figure 4 by the procedure given above. The correlation coefficient r with such approximation is r =.98. Then, for one recurrent unit of PP, the parameter d = 32.8 Å 3. If it is assumed that the given volume is contained in a sphere, then its diameter will be equal to ~6.33 Å, which is a reasonable value and corresponds to a slightly greater size than the size of a PP unit (4.6 Å; calculated in accordance with references [2] and [3]). CONCLUSIONS. The thermomechanical curves of recycled and virgin PP are practically identical. 2. The elastic modulus and the relaxation moduli of recycled PP are higher than those of virgin PP (Figure 7), which indicates the possibility of the lasting use of recycled PP for the production of articles operating under high loads in different deformation regimes. REFERENCES. M.N. Popova and D.V. Pashkova, Problems of recycling polymer waste from preventive medicine establishments. Ekologiya Promyshlennogo Proizvodstva, No., 24, p A.S. Askadskii and V.I. Kondrashchenko, Computational Materials Science of Polymers. Nauchnyi Mir, Moscow, A.A. Askadskii and V.I. Kondrashchenko, Computational Materials Science of Polymers. Cambridge Int. Sci. Publ., Cambridge, UK, G.I. Gurevich, Zhurn. Tekhn. Fiziki, 7, No. 2, 947, p A.A. Askadskii and M.P. Valetskii, Mekhanika Kompozit. Materialov, No. 3, 99, p. 44. T/58 International Polymer Science and Technology, Vol. 37, No. 9, 2